James is planning on building a swimming pool, enclosed by a baby gate, for his backyard. He knows that he will need a total of 54 feet to completely surround the pool with the gate. When measuring the length and width of the proposed pool area, James discovers that the length is double the width. What are the dimensions of the proposed swimming pool?

the length = 18 feet and width = 9 feet

Step-by-step explanation:

Step 1:

Assume

Length of the rectangle = b

Width of the rectangle = a

Step 2:

As mentioned in the question length is double the width therefore;

b = 2*a

Step 3:

as mentioned in the question James need total 54 feet to cover the pool that means the perimeter of the pool is 54 feet therefore perimeter formula can be used as follows;

P = 2a + 2b

54 = 2a + 2 (2a)

54 = 2a + 4a

54 = 6a

a = 54/6

a = 9 feet

Step 4:

Now again use equation from step b to find out the length;

b = 2a

take value of a from step 3

b = 2*9

b = 18 feet